Seven squares are drawn inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.

The centre square has the area of 1 (one) square unit.

Draw the diagram. You can download square dotty paper here.

What is the total area of the four outside triangles which are outlined in red?

Download the NRICH poster for this activity.

See Notes for Teachers and solutions.

3 Responses to Seven Squares

  1. Sirrah Galeni says:

    I could use this puzzle for my grade 7 classes. Using geoboards is the best way of approaching the problem, with square dotty paper on which to draw. Learners would then start on the inside square and draw it on their dotty paper.Next would follow the second square and so on to last and biggest one. At each stage they draw what they have built on their geoboards and count the number of squares. Ultimately they have to see a pattern which will help them to answer the question before they can reach the end of the puzzle (biggest square).

  2. Innocent Dlamini says:

    The activity involves geometric patterns, identifying patterns, establishing a rule which can be used to calculate the areas of the rest of the squares. One could exploit the activity to teach shapes such as squares and triangles.The idea of fractals seems to pop up as well.

  3. Zuko Manqaba says:

    I think it will be very nice and interesting if I use it with my grade 8 learners,but I think that they will understand it much more better if we can use the dotted paper rather than the squared paper as it has already have joined lines that may sometimes confuse them.With dotted paper they have to start by doing the first 1 by 1 unit square,followed by the second 1 which they will see clearly and so on and so on.The other thing that I think will be more convenient and helpful to my learners is the use of geoboards.

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